"Police are looking for his family, but so far they've not been able to trace them," said Abul Khair Nadim, the Chair of Musapur Union council, a local government body in the Chittagong division in southern Bangladesh, where Ullah's family originally lived.
Bangladesh's police chief told Reuters late on Monday that 27-year-old Ullah had no criminal record in his home country, which he last visited in September.
Ullah lived with his mother, sister and two brothers in Brooklyn and was a green card holder, said Shameem Ahsan, consul general of Bangladesh in New York.
Ahmad Ullah, a relative of Ullah, who Reuters tracked down on Tuesday, said his cousin's father had moved to the Bangladeshi capital of Dhaka with his family many years ago.
He said Ullah's father had passed away about five years ago, and that Ullah had been through a normal public school education in Bangladesh before moving to the United States.
Ullah, who had a homemade bomb strapped to his body, set off an explosion in an underground pedestrian corridor between New York's Times Square and the Port Authority Bus Terminal at rush hour, injuring himself and three others in what New York Mayor Bill de Blasio called an attempted terrorist attack.
A law enforcement official familiar with the investigation said investigators have found evidence that Ullah had watched Islamic State propaganda on the internet.
Bangladesh strongly condemned the attack in a statement saying, "A terrorist is a terrorist irrespective of his or her ethnicity or religion, and must be brought to justice."
International / Bangladesh
Bangladesh police looking for family, associates of New York bombing suspect
Akayed Ullah
Officials in Bangladesh are trying to track down the extended family and any known associates of Akayed Ullah, a Bangladeshi man US authorities say set off a homemade pipe bomb in a crowded New York City commuter hub on Monday.